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Weighted norm inequalities for maximal singular integrals with nondoubling measures

Guoen Hu, Dachun Yang (2008)

Studia Mathematica

Let μ be a nonnegative Radon measure on d which satisfies μ(B(x,r)) ≤ Crⁿ for any x d and r > 0 and some positive constants C and n ∈ (0,d]. In this paper, some weighted norm inequalities with A p ϱ ( μ ) weights of Muckenhoupt type are obtained for maximal singular integral operators with such a measure μ, via certain weighted estimates with A ϱ ( μ ) weights of Muckenhoupt type involving the John-Strömberg maximal operator and the John-Strömberg sharp maximal operator, where ϱ,p ∈ [1,∞).

Weighted norm inequalities for vector-valued singular integrals on homogeneous spaces

Sergio Antonio Tozoni (2004)

Studia Mathematica

Let X be a homogeneous space and let E be a UMD Banach space with a normalized unconditional basis ( e j ) j 1 . Given an operator T from L c ( X ) to L¹(X), we consider the vector-valued extension T̃ of T given by T ̃ ( j f j e j ) = j T ( f j ) e j . We prove a weighted integral inequality for the vector-valued extension of the Hardy-Littlewood maximal operator and a weighted Fefferman-Stein inequality between the vector-valued extensions of the Hardy-Littlewood and the sharp maximal operators, in the context of Orlicz spaces. We give sufficient...

Weighted Orlicz space integral inequalities for the Hardy-Littlewood maximal operator

S. Bloom, R. Kerman (1994)

Studia Mathematica

Necessary and sufficient conditions are given for the Hardy-Littlewood maximal operator to be bounded on a weighted Orlicz space when the complementary Young function satisfies Δ 2 . Such a growth condition is shown to be necessary for any weighted integral inequality to occur. Weak-type conditions are also investigated.

Weighted pseudo almost automorphic functions with applications to abstract dynamic equations on time scales

Chao Wang, Yongkun Li (2013)

Annales Polonici Mathematici

We propose a concept of weighted pseudo almost automorphic functions on almost periodic time scales and study some important properties of weighted pseudo almost automorphic functions on almost periodic time scales. As applications, we obtain the conditions for the existence of weighted pseudo almost automorphic mild solutions to a class of semilinear dynamic equations on almost periodic time scales.

Weighted Sobolev-Lieb-Thirring inequalities.

Kazuya Tachizawa (2005)

Revista Matemática Iberoamericana

We give a weighted version of the Sobolev-Lieb-Thirring inequality for suborthonormal functions. In the proof of our result we use phi-transform of Frazier-Jawerth.

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